Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\)
In this paper we study the continuation of harmonic functions in the ball to the entire harmonic functions in space \(\mathbb{R}^n\), \(n\geq 3\). The generalized order introduced by M.N. Seremeta has been used to characterize the growth of such functions. Moreover, the generalized order, genera...
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| Format: | Article |
| Language: | English |
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Publishing House of the Romanian Academy
2018-12-01
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| Series: | Journal of Numerical Analysis and Approximation Theory |
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| Online Access: | https://ictp.acad.ro/jnaat/journal/article/view/1166 |
| _version_ | 1818006616331517952 |
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| author | Devendra Kumar |
| author_facet | Devendra Kumar |
| author_sort | Devendra Kumar |
| collection | DOAJ |
| description |
In this paper we study the continuation of harmonic functions in the ball to the entire harmonic functions in space \(\mathbb{R}^n\), \(n\geq 3\).
The generalized order introduced by M.N. Seremeta has been used to characterize the growth of such functions. Moreover, the generalized order, generalized lower order and generalized type have been characterized in terms of harmonic polynomial approximation errors.
Our results apply satisfactorily for slow growth.
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| first_indexed | 2024-04-14T05:04:31Z |
| format | Article |
| id | doaj.art-5e330c35f5104a49a20a4d20561bf3b9 |
| institution | Directory Open Access Journal |
| issn | 2457-6794 2501-059X |
| language | English |
| last_indexed | 2024-04-14T05:04:31Z |
| publishDate | 2018-12-01 |
| publisher | Publishing House of the Romanian Academy |
| record_format | Article |
| series | Journal of Numerical Analysis and Approximation Theory |
| spelling | doaj.art-5e330c35f5104a49a20a4d20561bf3b92022-12-22T02:10:48ZengPublishing House of the Romanian AcademyJournal of Numerical Analysis and Approximation Theory2457-67942501-059X2018-12-01472Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\)Devendra Kumar0M.M.H.College In this paper we study the continuation of harmonic functions in the ball to the entire harmonic functions in space \(\mathbb{R}^n\), \(n\geq 3\). The generalized order introduced by M.N. Seremeta has been used to characterize the growth of such functions. Moreover, the generalized order, generalized lower order and generalized type have been characterized in terms of harmonic polynomial approximation errors. Our results apply satisfactorily for slow growth. https://ictp.acad.ro/jnaat/journal/article/view/1166approximation errorsentire harmonic functionsgeneralized ordergeneralized typeball of radius r |
| spellingShingle | Devendra Kumar Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\) Journal of Numerical Analysis and Approximation Theory approximation errors entire harmonic functions generalized order generalized type ball of radius r |
| title | Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\) |
| title_full | Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\) |
| title_fullStr | Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\) |
| title_full_unstemmed | Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\) |
| title_short | Generalized growth and approximation errors of entire harmonic functions in \(R^n\), \(n \geq 3\) |
| title_sort | generalized growth and approximation errors of entire harmonic functions in r n n geq 3 |
| topic | approximation errors entire harmonic functions generalized order generalized type ball of radius r |
| url | https://ictp.acad.ro/jnaat/journal/article/view/1166 |
| work_keys_str_mv | AT devendrakumar generalizedgrowthandapproximationerrorsofentireharmonicfunctionsinrnngeq3 |